This is just my personal experience . . .
I have an aunt named
Penny. Her actual given name is
Helen Gisela, but when she was born someone pointed out that her hair was the colour of a new penny, and the nickname stuck and was used as if it were her first name.
So, "
Penny" could be a nickname of the "Shorty" or "Bluey" kind, a description or reference nickname rather than one pertaining to the actual given name.
Have you seen it more than once as a nickname for
Elizabeth?